Quantum and classical spins on the spatially distorted kagomé lattice: Applications to volborthiteCu3V2O7(O

Abstract

In Volborthite, spin-1/2 moments form a distorted Kagomé lattice, of corner sharing isosceles triangles with exchange constants J on two bonds and J ′ on the third bond. We study the properties of such spin systems, and show that despite the distortion, the lattice retains a great deal of frustration. Although sub-extensive, the classical ground state degeneracy remains very large, growing exponentially with the system perimeter. We consider degeneracy lifting by thermal and quantum fluctuations. To linear (spin wave) order, the degeneracy is found to stay intact. Two complementary approaches are therefore introduced, appropriate to low and high temperatures, which point to the same ordered pattern for J ′ > J. In the low temperature limit, an effective chirality Hamiltonian is derived from non-linear spin waves which predicts a transition on increasing J ′ /J, from √ 3 × √ 3 type order to a new ferrimagnetic striped chirality order with a doubled unit cell. This is confirmed by a large-n approximation on the O(n) model on this lattice. While the saddle point solution produces a line degeneracy, O(1/n) corrections select the non-trivial wavevector of the striped chirality state. The quantum limit of spin-1/2 on this lattice is studied via exact small system diagonalization and compare well with experimental results at intermediate temperatures.We suggest that the very low temperature spin frozen state seen in NMR experiments may be related to the disconnected nature of classical ground states on this lattice, which leads to a prediction for NMR line shapes.

Topological magnetic excitations on the distorted kagomé antiferromagnets: Applications to volborthite, vesignieite, and edwardsite

“…The classical configuration is now a canted coplanar/noncollinear spins for δ > 1/2 [62]. However, it also has an extensive degeneracy as in the ideal kagomé Heisenberg antiferromagnets.…”

“…Let us start from what is known for distorted kagomé antiferromagnets at D ij = h = 0 [62]. In this case, the Hamiltonian can be written as…”

“…1. The last term is the out-of-plane external magnetic field H = hẑ and h = gµ B H. The Hamiltonian (1) is applicable to volborthite [60][61][62][63][64] and other forms of Hamiltonian have also been proposed for volborthite [65][66][67]. The out-of-plane DM interaction is always present on the kagomé lattice and it stabilizes the coplanar/noncollinear spin configuration [13].…”

Correlations in the Ising antiferromagnet on the anisotropic kagome lattice

“…Recent experimental work on the mineral volborthite has stimulated several theoretical investigations of the Heisenberg antiferromgnet on the spatially anisotropic kagome lattice, figure 1, [1,2,3]. In this model, the exchange coupling in one of the three lattice directions (J) differs from the couplings in the two other directions (J ′ ).…”

Classification of quantum phases for the star-lattice antiferromagnet via a projective symmetry group analysis

“…17 Therefore, systematic studies of a variety of frustrated magnets with possibly different spin interactions and/or with different underlying lattice structures would be extremely useful. 18,19 In this regard, the recent discovery of the iron acetate may present one of such useful examples for a two-dimensional frustrated lattice. 1 Here, Fe III spin-5/2 moments reside on the star lattice as shown in Fig.…”